In this paper, we study flag structures of matroid base polytopes. We describe faces of matroid base polytopes in terms of matroid data, and give conditions for hyperplane splits of matroid base polytopes. Also, we show how the cd-index of a polytope can be expressed when a polytope is split by a hyperplane, and apply these to the cd-index of a matroid base polytope of a rank 2 matroid.

We show the existence of a polynomial-size extended formulation for the base polytope of a (k, l)-sparsity matroid. For an undirected graph G = (V,E), the size of the formulation is O(|V ||E|) when k ≥ l and O(|V ||E|) when k ≤ l. To this end, we employ the technique developed by Faenza et al. recently that uses a randomized communication protocol.

This paper presents an original definition of data representativeness. The representativeness of each datum in a dataset is a meaningful notion quantified by a degree computed by aggregating fuzzy subsets. These fuzzy subsets are obtained by fuzzifying data in a robust way. We illustrate the usefulness of the representativeness by presenting applications for statistical location estimation,and ...

In this paper, the fuzzy nonlinear programming problem is discussed. In order to obtain more accurate solution, the properties of fuzzy set and fuzzy number with linear membership function and fuzzy maximum decision maker is utilized to fuzzifying the crisp problem . An example is provided to show the effectiveness of the proposed method.

For an integer l ≥ 2, let U(l) be the class of matroids with no U2,l+2-minor. A matroid in U(l) is extremal if it is simple and has no simple rank-preserving singleelement extension in U(l). An amalgam of two matroids is a simultaneous extension of both on the union of the two ground sets. We study amalgams of extremal matroids in U(l): we determine which amalgams are in U(l) and which are extr...

In this paper we consider the problem of finding the densest subset subject to co-matroid constraints. We are given a monotone supermodular set function f defined over a universe U , and the density of a subset S is defined to be f(S)/|S|. This generalizes the concept of graph density. Co-matroid constraints are the following: given matroid M a set S is feasible, iff the complement of S is inde...

The notion of matroid has been generalized to Coxeter matroid by Gelfand and Serganova. To each pair (W, P) consisting of a finite irreducible Coxeter group W and parabolic subgroup P is associated a collection of objects called Coxeter matroids. The (ordinary) matroids are a special case, the case W = An (isomorphic to the symmetric group Symn+1) and P a maximal parabolic subgroup. The main re...

Uncertainty is an inherent property of all living systems. Curiously enough, computational models inspired by biological systems do not take, in general, under consideration this essential aspect of living systems. In this paper, after introducing the notion of a multi-fuzzy set (i.e. an orthogonal approach to the fuzzification of multisets), we introduce two variants of P systems with fuzzy co...